US8725283B2 - Generalized kinematics system - Google Patents
Generalized kinematics system Download PDFInfo
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- US8725283B2 US8725283B2 US11/833,971 US83397107A US8725283B2 US 8725283 B2 US8725283 B2 US 8725283B2 US 83397107 A US83397107 A US 83397107A US 8725283 B2 US8725283 B2 US 8725283B2
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/406—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by monitoring or safety
- G05B19/4069—Simulating machining process on screen
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/408—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by data handling or data format, e.g. reading, buffering or conversion of data
- G05B19/4086—Coordinate conversions; Other special calculations
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/34—Director, elements to supervisory
- G05B2219/34202—Reusable software, generic resource model library
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/35—Nc in input of data, input till input file format
- G05B2219/35346—VMMC: virtual machining measuring cell simulate machining process with modeled errors, error prediction
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/36—Nc in input of data, input key till input tape
- G05B2219/36252—Generate machining program based on a simulation to optimize a machine parameter
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/36—Nc in input of data, input key till input tape
- G05B2219/36276—Program virtual, logical tools, select tool from tables
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- Engineering & Computer Science (AREA)
- Human Computer Interaction (AREA)
- Manufacturing & Machinery (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Numerical Control (AREA)
Abstract
Description
-
- ID
- Type (linear/rotary/tilt/spindle)
- Direction
- Coordinate location (centerline if rotational axis)
- Limits
- Maximum velocities
- Connection (whether the axis is connected to the tool or to the part)
-
- Shortest angular traverse,
- Interpolation on/off
- Interpolation type if on
- Tilt axis preference direction or off or force use of preference direction
Multiple Instances of the Generalized Kinematics Library
- Axis ID=integer {0,1,2,3,4,5,6,7} corresponding to {X,Y,Z,A,B,C,S}
- Name=string {“X”,“Y”,“Z”,“A”,“B”,“C”,“S”)
- Type=enumeration {Linear, Rotary, Tilt, Spindle}
- Position=axis position
- Matrix=axis transformation matrix
- Connection=enumeration {Tool, Part}
- MinPosition=lower bound of motion
- MaxPosition=upper bound of motion
- AxisLimitsExists=Boolean {True, False}
- InitialMachineDirection Vector=Vector in Machine reference frame representing positive axis movement direction. For rotation axes, vector direction of axis centerline for Right-hand positive rotation.
- MaxContourSpeed=interpolation speed
- MaxRapidSpeed=rapid move speed
Methods: - Several methods are included in the Axis base class including Set( ) and Get( ) functions for each of the above data.
- Location=spindle coordinate system origin with respect to axis it is connected to
Methods: - SetAxisS( )=initialization function
- SetInitSpindleAxisDirectionWrtMachine(DirectionVector)=function to set InitialMachineDirection Vector from base Axis class
- SetLocationWrtLastAxis( )=function to set the location of the spindle coordinate system with respect to the last axis it is connected to
- Translate( )=functions to translate a vector or multiply a matrix by the linear axis translation matrix
- SetAxis(x,y,z)=initialization functions
- Centerline=Location of axis of rotation
Methods: - SetAxis(a,b,c)=Initialization functions
- Rotate( )=functions to rotate a vector or multiply a matrix by the rotation
- GetPerpendicularDistanceToAxis(Point)=function returns perpendicular radial distance to axis of rotation
-
- wherein is a column vector representing the location of the tool tip in the spindle coordinate system;
- [Transformspindle] is the transformation from the spindle coordinate system to the rotary B-axis coordinate system;
- [TransformB] is the transformation from the rotary B-axis coordinate system to the z-axis coordinate system;
- [TransformZ] is the transformation from the z-axis coordinate system to a machine coordinate system; and
- is a column vector representing the tool tip position in the machine coordinate system.
-
- wherein is a column vector representing the location of the point of the part in the workpiece coordinate system if no transform planes are active or to the top transform plane in the TransformMatrixStack if at least one transform plane is active;
- [Pre-TransformPlaneMatrixStack] is the patterning transformations applied to the input position;
- [TransformPlaneMatrixStack] is the concatenated TransformPlaneMatrixStack matrix transformation from the system defined in the patterning transformation stack to the part setup coordinate system;
- [PartSetupMatrix] is the transformation from the part coordinate system to the C-axis coordinate system;
- [TransformC] is the transformation from the rotary C-axis coordinate system to the x-axis coordinate system;
- [Transformx] is the transformation from the x-axis coordinate system to the y-axis coordinate system;
- [Transformy] is the transformation from the y-axis coordinate system to the machine reference coordinate system; and
- is a column vector representing the part point position in the reference machine coordinate system.
wherein
- P=surface contact point on workpiece;
- N=surface normal vector at P;
- T=tool axis vector;
- R=tool outer major radius;
- r=Radius of tool
Equation 3 describes the movement from thesurface contact point 414 to the tool bottom center point. The term r×({circumflex over (N)}−{circumflex over (T)}) combines 414→418 and 420→416 and the term
determines
wherein the
- TiltAngle is the rotary angle of the B-axis;
- 434 is the input tool vector in the machine coordinate system 436; and
- 432 is the spindle axis of rotation with respect to the machine coordinate system when the Tilt Axis angle is zero.
The component of the
The component of the
The tool vector projected in the TiltAxis and CrossVector0 plane is expressed by equation 8 and labeled as 446 in
wherein
mag=√{square root over ((ToolVectorTCR[0])2+(ToolVectorTCR[1])2)}{square root over ((ToolVectorTCR[0])2+(ToolVectorTCR[1])2)} (9)
The rotary angle of C-
ΔRotaryAngle1=RotaryAngleNext−RotaryAngleLast (11)
wherein
- ΔRotaryAngle1 is the change in the rotary angle
- RotaryAngleNext is the rotary angle being considered; and
- RotaryAngleLast is the rotary angle of the previous position.
ΔTiltAngle1=TiltAngleNext−TiltAngleLast (12)
wherein - ΔTiltAngle1 is the change in the tilt angle;
- TiltAngleNext is the tilt angle being considered; and
- TiltAngleLast is the tilt angle of the previous position.
Calculate the alternate rotary solution.
ΔTiltAngle2=AlternateTiltAngle−TiltAngleLast (13)
wherein
- AlternateTiltAngle is the alternate angular solution;
- ΔTiltAngle2 is the difference between the last tilt axis position and the alternate angular solution.
TransformedPartPointMach=PartMatrixStack.ForwardTransform(PartPointWP)
TransformedToolTipMach=ToolMatrixStack.ForwardTransform(ToolTipSpindleZeroPoint)
DeltaVectorMach=TransformedPartPointMach−TransformedToolTipMach (14-16)
AlternateRotaryAngle=ConvertToZeroTo2PI(RotaryAngle+π)
AlternateTiltAngle=(SingularityTiltAngle−TiltAngle)+SingularityTiltAngle (17, 18)
wherein
- RotaryAngle is the rotary angle for
solution 1; - TiltAngle is the tilt angle for
solution 1; and - SingularityTiltAngle is the angle of the tilt axis at the singularity point.
Interpolation Relative to the Machine Singularity Point
If (AngleLastAndNextSurfaceNormal≠0) then the surface normal vector for the prior position and the surface normal vector for the next interpolated position are not collinear.
wherein
- is the vector about which the prior position surface normal vector will rotate is determined based on the relationship in equation (19)
and SurfNormRotationAngle is the magnitude of the angular rotation based on the relationship in equation 20
wherein
Δ1=ΔSingularityToLastTiltAngle=LastTiltAngle−SingularityTiltAngle
Δ2=ΔSingularityToNextTiltAngle=NextTiltAngle−SingularityTiltAngle
Δ3=ΔTotalTiltAngleTraverse=|ΔSingularityToLastTiltAngle|+|ΔSingularityToNextTiltAngle| (21-23)
If (AngleLastAndNextToolVector≠0) then the tool vector for the prior position and the tool vector for the next interpolated position are not collinear.
wherein
- is the vector about which the prior position tool vector will rotate is determined based on the relationship in equation 27
and ToolVectorRotationAngle is the magnitude of the angular rotation based on the relationship in
wherein
Δ1=ΔSingularityToLastTiltAngle=LastTiltAngle−SingularityTiltAngle
Δ2=ΔSingularityToNextTiltAngle=NextTiltAngle−SingularityTiltAngle
Δ3=ΔTotalTiltAngleTraverse=|ΔSingularityToLastTiltAngle|+|ΔSingularityToNextTiltAngle| 29-31
(RotaryRadialDistance>0 and RotaryRadialDistance≧ChordError and |Δ4|>0) (33)
the number of iterations is determined by equation 34
wherein
- the ceil( ) function rounds up to the next integer;
- ChordError is the operator specified tolerance;
Δ4=ShortestAngularTraverse(NextRotaryAngle−LastRotaryAngle) (35),
wherein the function ShortestAngularTraverse( ) returns the angular difference between two angular positions that is less than or equal to 180 degrees. If the relationship in equation 33, is not satisfied, the interpolation method sets the number of iterations to one.
Number of Interpolation Steps—Fixed Angular Step
It should be noted that angular step (θstep) is less than or equal to the FixedRotaryAngularStep specified by the operator.
If (Δ4previous<0) then Δ4new=Δ4previous+2π; or
If (Δ4previous>0) then Δ4new=Δ4previous−2π.
Note that Δ4 cannot equal zero; otherwise there would be no rotation about the singularity point. If this attempt fails due to a position being outside of the machine limits, then both interpolation directions cannot be executed and the method throws an error of machine out of limits.
wherein
- #Iterations is the number of iterations;
- NextToolVector is a unit vector in the direction of the second tool position tool vector;
- LastToolVector is a unit vector in the direction of the first tool position tool vector; and
- MaxAngleStep is the desired angular step.
wherein
- #IterationsSurfNormal is the number of iterations based on the surface normals;
- LastSurfaceNormal is a unit vector in the direction of the surface normal for the first position;
- NextSurfaceNormal is a unit vector in the direction of the surface normal for the second position; and
- MaxAngleStep is the desired angular step.
The number of iterations then is chosen as the larger of the number of iterations determined in equation 39 and equation 40, as represented by equation 41.
TimeStepFromLastToNext=GetMinTimeStepBetweenPositions(LastPosition,NextPosition,WorkpieceRelativeFeedrate) (42)
wherein
- TimeStepFromLastToNext is the time step from the last position to the next position specified in the part program;
- LastPosition corresponds to the first position;
- NextPosition corresponds to the second position; and
- WorkpieceRelativeFeedrate corresponds to the feedrate of the tool tip relative to the workpiece specified in the part program.
wherein
- #Iterations is the number of iterations; and
- MaxTimeStep corresponds to the interpolation time step specified by an operator input parameter.
wherein
- AngleLastAndNextToolVector is the angle between the prior position and the next interpolated position;
- LastToolVector is the tool vector for the prior position; and
- NextToolVector is the tool vector for the next interpolated position.
Interpolation of the Tool Vector
wherein CrossVector1 is the vector (in workpiece coordinates) about which the prior position tool vector will rotate as the tool positions are interpolated;
- LastToolVector is the tool vector for the prior position; and
- NextToolVector is the tool vector for the next interpolated position.
wherein
- AngleLastAndNextSurfaceNormal is the angle between the prior position surface normal and the next interpolated position surface normal;
- LastSurfaceNormal is the surface normal for the prior position; and
- NextSurfaceNormal is the surface normal for the next interpolated position.
If (AngleLastAndNextSurfaceNormal=0) then the surface normal vector for the prior position and the surface normal vector for the next interpolated position are collinear. If (AngleLastAndNextSurfaceNormal≠0) then the surface normal vector for the prior position and the surface normal vector for the next interpolated position are not collinear.
wherein CrossVector2 is the vector (in workpiece coordinates) about which the prior position surface normal vector will rotate as the tool positions are interpolated;
- LastSurfaceNormal is the surface normal vector for the prior position; and
- NextSurfaceNormal is the surface normal vector for the next interpolated position.
If (AngleLastAndNextToolVector≠0) for a given iteration then the interpolated tool vector is determined based on the relationship in equation 49
wherein
- InterpolatedToolVector corresponds to the interpolated tool vector;
- ToolVectorRotationAngle is the angle the tool vector is to rotated and is determined based on the relationship in equation 50; and
- RotateAboutCrossVector1 is a function that rotates the LastToolVector about CrossVector1 through an angle equal to the value of ToolVectorRotationAngle.
The ToolVectorRotationAngle is determined based on the relationship in equation 50
If (AngleLastAndNextSurfaceNormal≠0) for a given iteration then the interpolated surface normal vector is determined based on the relationship in equation (53)
wherein
- InterpolatedSurfaceNormal corresponds to the interpolated surface normal vector;
- SurfaceNormalRotationAngle is the angle the surface normal vector is to be rotated and is determined based on the relationship in equation 54; and
- RotateAboutCrossVector2 is a function that rotates the LastSurfaceNormal about CrossVector2 through an angle equal to the value of SurfaceNormalRotationAngle.
The SurfaceNormalRotationAngle is determined based on the relationship in equation 54
Δ5=(NextTiltAngle−LastTiltAngle) (56)
Δ4=(NextRotaryAngle−LastRotaryAngle) (57)
MaxRotaryRadialDistance=max(RotaryRadialDistance1,RotaryRadialDistance2) (58)
wherein
- RotaryRadialDistance1 is the perpendicular radial distance of the tool tip to the rotary axis centerline of last position (This may be the last position computed in the
Stage # 1 Tool Vector interpolation method.); and - RotaryRadialDistance2 is the perpendicular radial distance of the tool tip to the rotary axis centerline of next position (This may be the next position computed in the
Stage # 1 Tool Vector interpolation algorithm).
MaxTiltRadialDistance=max(TiltRadialDistance1,TiltRadialDistance2) (59)
- TiltRadialDistance1 is the perpendicular radial distance of the tool tip to the tilt axis centerline of last position (This may be the last position computed in the
Stage # 1 Tool Vector interpolation method.); and - TiltRadialDistance2 is the perpendicular radial distance of the tool tip to the tilt axis centerline of last position (This may be the next position computed in the
Stage # 1 Tool Vector interpolation method).
(MaxRotaryRadialDistance>0 and MaxRotaryRadialDistance≧ChordError and |Δ4|>0) (60)
If the relationship in equation 60 is true, then the number of iterations is determined based on equation 61
#RotaryIterations=1 (62)
(MaxTiltRadialDistance>0 and MaxTiltRadialDistance≧ChordError and |Δ5|>0) (63)
If the relationship in equation 63 is true, then the number of iterations is determined based on equation 64
#TiltIterations=1 (65)
#Iterations=max(#RotaryIterations,#TiltIterations) (66)
ΔToolTipWP=(NextToolTipWP−LastToolTipWP)/#Iterations (67)
ΔRotaryAngle=(NextRotaryAngleMach−LastRotaryAngleMach)/#Iterations (68)
ΔTiltAngle=(NextTiltAngleMach−LastTiltAngleMach)/#Iterations (69)
InterpolatedToolTipWP=LastToolTipWP (70)
InterpolatedRotaryAngleMach=LastRotaryAngleMach (71)
InterpolatedTiltAngleMach=LastTiltAngleMach (72)
InterpolatedToolTipWP=InterpolatedToolTipWP+ΔToolTipWP (73)
InterpolatedRotaryAngleMach=InterpolatedRotaryAngleMach+ΔRotaryAngle (74)
InterpolatedTiltAngleMach=InterpolatedTiltAngleMach+ΔTiltAngle (75)
(|Δ4|>0) (76)
If the relationship in equation 76 is true, then the number of iterations is determined based on equation 77
#RotaryIterations=1 (78)
(|Δ5|>0) (79)
If the relationship in equation 79 is true, then the number of iterations is determined based on equation 80
#TiltIterations=1 (81)
#Iterations=max(#RotaryIterations,#TiltIterations) (82)
ΔToolTipWP=(NextToolTipWP−LastToolTipWP)/#Iterations (83)
ΔRotaryAngle=(NextRotaryAngleMach−LastRotaryAngleMach)/#Iterations (84)
ΔTiltAngle=(NextTiltAngleMach−LastTiltAngleMach)/#Iterations (85)
InterpolatedToolTipWP=LastToolTipWP (86)
InterpolatedRotaryAngleMach=LastRotaryAngleMach (87)
InterpolatedTiltAngleMach=LastTiltAngleMach (88)
InterpolatedToolTipWP=InterpolatedToolTipWP+ΔToolTipWP (89)
InterpolatedRotaryAngleMach=InterpolatedRotaryAngleMach+ΔRotaryAngle (90)
InterpolatedTiltAngleMach=InterpolatedTiltAngleMach+ΔTiltAngle (91)
CurrentPoint=ToolBottomCenterSpindle (92)
CurrentPoint=ToolMatrixStack[i]→GetMatrix( )*CurrentPoint (93)
RotaryRadialDistance=ToolMatrixStack[i]→GetPerpendicularDistanceToAxis(CurrentPoint) (94)
TiltRadialDistance=ToolMatrixStack[i]→GetPerpendicularDistanceToAxis(CurrentPoint) (95)
Once the Tool Matrix Stack is traversed, CurrentPoint holds the value of the tool tip with respect to the machine reference coordinate system. Further, in the case of
Matrix=PartMatrixStack[i]→GetMatrix( ) Matrix.InvertRigidTransformation( ) CurrentPoint=Matrix*CurrentPoint (96)
RotaryRadialDistance=PartMatrixStack[i]→GetPerpendicularDistanceToAxis(CurrentPoint) (97)
TiltRadialDistance=PartMatrixStack[i]→GetPerpendicularDistanceToAxis(CurrentPoint) (98)
Once the Part Matrix Stack is traversed, CurrentPoint holds the value of the tool tip with respect to the workpiece coordinate system.
Compute and Clamp Time Step Using Max Axes Speeds
TimeStep=ComputeTimeStepForConstantWorkpieceFeedrate( ) (99)
wherein
ΔAxisMove=|NextPosition.MachinePosition[i]−LastPosition.MachinePosition[i]| (101)
MaxAxisSpeed=Axis[i]→GetMaxSpeed( ) (102)
The value for the time step is given by equation 103.
Homogeneous Transformation Matrix and Matrix Stacks
wherein R is the rotation sub-matrix,
- t is the translation matrix,
- s is the shear matrix, and
- k is the scaling matrix.
The correspondence between the Boolean Decision Matrix and the Transformation Matrix is one-to-one as shown in FIG. 26.:
Relationship of Sub-Matrices
T 3 =T 1 ·T 2 (107)
Inserting 105 into 107 gives:
R 3 =R 1 ·R 2 +t 1 ·s 2 T =R 1 ·R 2, (109)
Next, translation sub-matrix.
t 3 =R 1 ·t 2 +t 1 ·k 2, (110)
Then, shear sub-matrix.
s 3 T =s 1 T ·R 2 +k 1 ·s 2 T=0T, (111)
Last, scaling
k 3 =s 1 T ·t 2 +k 1 ·k 2 =k 1 ·k 2. (112)
-
Property 1. Identity operand of multiplication (i.e. value of 1) contributes the other matrix's operand directly to the resulting matrix. -
Property 2. Zero operand of multiplication results in a zero in the resulting matrix.
Processes with the Sub-Matrices
- 1. When the situation fits
Property 1, the multiplication is skipped. - 2. When the situation fits
Property 2, the multiplication and addition are skipped.
- 1. R3=R2 if dR1=true.
- 2. R3=R1 if dR2=true.
- 3. Skip R1·t2 if dR1=true.
- 4. Skip addition if dt1=true or dt2=true.
T 2 =T 1 −1 (113)
Inserting 105 into 113 gives:
wherein
R 2 =R 1 T (115)
t 2 =−R 2 ·t 1 (116)
s 2 T =s 1 T=[0 0 0] (117)
k 2 =k 1=1 (118)
Determination of Part Setup Matrix
WorkpieceZeroTableLastAxis=PartMatrixStack.InverseMatrix( )|PartSetupPositions*ToolMatrixStack.ForwardMatrix( )|PartSetupPositions*ToolTipTransformMatrix*[0 0 0 1]T (119)
wherein
PartMatrixStack.InverseMatrix( )|ZeroCalibration is the Part Matrix Stack inverse transformation matrix evaluated when all part axes are set to their Part Setup Axes Positions. (120)
ToolMatrixStack.ForwardMatrix( )|PartSetupPositions is the Tool Matrix Stack forward transformation matrix stack evaluated when all tool axes are set to their Part Setup Axes Positions. (121)
ToolTipTransformMatrix is the transformation from the tool tip coordinate system to the Spindle Axis coordinate system. It is a simple translation matrix containing the offset of the tool tip relative to the Spindle Axis coordinate system.
WorkpiecePointTableLastAxis=PartMatrixStack.InverseMatrix( )|PartSetupPositions*ToolMatrixStack.ForwardMatrix( )|PartSetupPositions*ToolTipTransformMatrix*WorkpiecePointWorkpiece
Therefore, the Part Setup Matrix may be determined with the following equation, noting that the Part Setup Matrix in the Part Matrix Stack is a 4×4 Identity matrix.
PartSetupMatrix=PartMatrixStack.InverseMatrix( )|PartSetupPositions*ToolMatrixStack.ForwardMatrix( )|PartSetupPositions*ToolTipTransformMatrix
The new Part Setup Matrix is then pushed onto the top of the Part Matrix Stack.
Claims (16)
Priority Applications (10)
Application Number | Priority Date | Filing Date | Title |
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US11/833,971 US8725283B2 (en) | 2006-08-04 | 2007-08-03 | Generalized kinematics system |
JP2009523079A JP2010513996A (en) | 2006-08-04 | 2007-08-06 | General kinematics system |
CN200780029074A CN101796462A (en) | 2006-08-04 | 2007-08-06 | Generalized kinematics system |
CA2659508A CA2659508C (en) | 2006-08-04 | 2007-08-06 | Generalized kinematics system |
EP07813808.8A EP2057516B1 (en) | 2006-08-04 | 2007-08-06 | Generalized kinematics system |
SG2011056421A SG173425A1 (en) | 2006-08-04 | 2007-08-06 | Generalized kinematics system |
PCT/US2007/075274 WO2008019336A2 (en) | 2006-08-04 | 2007-08-06 | Generalized kinematics system |
TW096128899A TWI381256B (en) | 2006-08-04 | 2007-08-06 | System, method, and computer readable medium for controlling the movement of a plurality of moveable axes of a machine tool system |
US12/765,352 US9459616B2 (en) | 2007-08-03 | 2010-04-22 | Universal conversational programming for machine tool systems |
US12/765,586 US9588511B2 (en) | 2007-08-03 | 2010-04-22 | Virtual machine manager |
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US11/833,971 US8725283B2 (en) | 2006-08-04 | 2007-08-03 | Generalized kinematics system |
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CA (1) | CA2659508C (en) |
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Publication number | Priority date | Publication date | Assignee | Title |
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CA2659508A1 (en) | 2008-02-14 |
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